The 44-year-old has led the Terriers to the top of the Championship courtesy of eight wins from the opening 11 games of the season.
This has alerted a host of top clubs, with Aston Villa believed to be keen on Wagner replacing Roberto Di Matteo following the Italian’s dismissal on Monday.
Villa’s interest follows that of Derby County last week in the wake of Nigel Pearson’s suspension.
Sources at the John Smith’s Stadium, however, indicate that the club are unconcerned about the situation with The Yorkshire Post understanding there has been no contact between Villa and Huddersfield.
Nor, it seems, would the Terriers welcome any approach for a manager who has raised hopes of a first concerted push for the top flight since the 1999-2000 season.
Steve Bruce was in charge of Huddersfield back then and the former Hull City chief is also believed to be firmly on Villa’s radar.
The 54-year-old has been out of work since quitting Hull in June amid a fall-out with the club’s hierarchy over transfers.
Appointing Bruce, a former Birmingham City manager, would not be without its problems, but a CV that contains four promotions to the Premier League could provide a persuasive case to Villa owner Tony Xia, who is understood to have timed Di Matteo’s departure to allow interviews to take place during the international break.
For his part, Wagner was keen not to become embroiled in the speculation over a possible exit from Huddersfield when Derby’s interest became public last week.
”My future is irrelevant,” was his firm response.
Wagner was appointed by Town last November and signed a new contract during the summer.
He has continually spoken of his job at the Terriers being a “long-term project” and admitted last month how immersed he is in the task of bringing success to the club.
“Most of my time I spend here at the club,” he said before the trip to Brighton. “I have been to the centre of Leeds twice, to York twice and to Liverpool, on Anfield Road, three times. But the rest is here.”